A pyramid has a square base. Find its SURFACE AREA if its slant height
is 10 centimeters and the sides of its base are 5 cm long.

Hello.

Here are the general formulae for the surface area of pyramid:

Surface Area = Lateral Area + Base Area
Lateral Area = 1/2 * Pb * Hs
Perimeter Base ( Pb ) = 2a + 2b
Base Area = a * b
http://microgeometry.netfirms.com/content/pyramid.html

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So...

Base Area = a * b
          = 5 * 5
          = 25 sq cm


Perimeter Base ( Pb ) = 2a   + 2b
                      = 2(5) + 2(5)
                      = 10   + 10
                      = 20 
             

Lateral Area = 1/2 * Pb * Hs
             = 1/2 * 20 * 10
             = 100 sq cm


Surface Area = Lateral Area + Base Area
             = 100 sq cm    + 25 sq cm
             = 125 sq cm


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Another way of solving this is:

"The surface area, SA, of a regular square pyramid is given by: SA = s^2 + 2sl,
where s is the length of the side of the base l is the slant height. "
http://www.accd.edu/sac/slac/PDF/math0301/12-4_Solids.pdf


SA = s^2 + 2sl
SA = 5^2 + 2(5)(10)
SA = 5^2 + (10)(10)
SA = 25  + 100
SA = 125 sq cm


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search strategy:
"surface area"  "regular square pyramid" "slant height"

I hope this helps.